SPECTRAL-DOMAIN ANALYSIS OF FIN-LINE RESONATORS AKEILESE: KUMAR AGRAWAL DEPARTMENT OF ELECTRICAL ENGINEERING

Transcription

1 SPECTRAL-DOMAIN ANALYSIS OF FIN-LINE RESONATORS by AKEILESE: KUMAR AGRAWAL DEPARTMENT OF ELECTRICAL ENGINEERING Dissertation submitted in Fulfilment of the Requirement the DezTree of of DOCTOR OF PHILOSOPHY to the INDIAN INSTITUTE OF TECHNOLOGY NEW DELHI-16 4th Jan,t. 1984

2 CERTIFICATE This is to certify that the dissertation entitled "Spectral-Domain Analysis of Fin-Line Resonators", which is being submitted by Mr. AKHILESH KUMAR AGRAWAL to the Indian Institute of Technology, Delhi, for the award of decree of Doctor of Philosophy, is a record of bonaf1(1(; research work carried out by him unr my flid -Ince and supervision. In my opinion, this dissertation has reached the Jndnrd fulii.11i.nc; the requirements of th, rer.ulations reinti.i: to tle dtlree. The results containe,), in it have not 'Cf2.11 sulwiitted, in part or in lull, to nary other univ(.rity or institute for the nwnrd of any (ierr(j- or olpt (Bharathi Mint) Professor Centre for Applied Research in Electronics Department of Mectrical Engineering Indian Institute of TechnoloFy,Dolhi New Do thi /4 SKI

3 ACKNOWLEDGEMENTS I am grateful to Professor Bharathi that for her precious time, guidance, and for her critical appraisal of this work. I wish to express my gratitude to the staff of of the Centre for Applied Research in Electronics, in particular to Mr. S.P. Chakraborty and Mr. R.S.Raghav for their help. I wish to express my appreciation to the staff of the Computer Center for their cooperation and help, to Mr Harish Bhatia for typing the manuscript, and to Mr. R. Kapoor for the drawings. I am grateful to Dr. O.S. Sahgal, Principal, Funjat Engineering College, Chandigarh for his constant encouragement. A.KHILESH KUMAR AGRAWAL

4 Abstract This thesis presents an analytical study of single and coo led rectanular slot resonators in fin-line confiiuration. The analysis is based on Galerkin's method in Fourier transform domain. ExpeTimental verification of the theoretical results on the resonant frequencies of sin le slot resonators in fin-line as well as in open configuration is provi::od. The spectral-domain analysis of a single slot resonator in unilateral fin-line is carried out first and a characteristic equation is derived for determining its resonant frequency. The characteristic equati,11 for resonators in bilateral fin-line is obtained by a suitable modification in the boundary conditions and structural parameters. 4 considering the walls of the shielding enclosure sufficiently far apart, so that they have negligible influence on the slot fields, the above characteristic equations are used to determine the resonant frequencies of single slo t resonator and broadside couijed resonators in op en configuration. The characteristic equation for the determination of resonant frt 4uuncy is modified to determine the wavelons;th in each cr_'afioratin having an infinitely long slot. With this informati:)n the end-corrections in slot resonators in f i It -1 inc con fi t i ns are computed a s imc t j it of the structural parameters.

5 Cflracteristic equations to determine the even-.!nd edd-filoe resonant frequencies of coupled rectangular slot resonters fin-ijne/op,7m configurations are derived_ he sr: die obtained. as a modification of the characteristic equation of the corresponding single resonator configuration by the P;roliction of shifting theorem. Three cases of coupling configurations have been considered in unilateral fin-line as well as in open slot configurations. They are (i) parallel-coupled resonators (ii) parallel-coupled offset resonators, and (iii) end-coupled resonators. Effects of structural parameters on the even- and odd-mode resonant frequencies and end-corrections for the above thr.c tyje :: ul ewipled renonmorn in unilntern1 both centered and off-centered fin locations have been studied. Numerical results on the resonant frequencies of coupled resonators in open configuration are also reported. class of resonators using double dielectric fin-line with on intrvonin.7 airgap between the two dielectric substrates studied. Inc air 1!.:ip between the sniintrnts.1;ervc. :IF, a variable N:raT..(Ar and provides flexibility in the design of resonant structures. Both singl:j as well as edgc-coupled resonators are considered. The two substrates carry identical resonator r:ttern3 which form mirror images of mid; othur. The variations of resonant frequencies are studied as a function of the air gap for two cases; namely, (i) with fins on two substrates iacin ceh c'thur (ii) with fins focing ti

6 adjacent sicl w3lls nf the guide. In the second case, when the air set equal tc2 zere, t structure reduces to bilateral i,esenant frequencies resonators in bilateral configuration have also been computed. In order to verify the accuracy of numerical results, experiments wore carried out en some sample resonator configurations. The effect of side walls on the resonant frequency of single slot resonator has been studied experimntally. IZesnant frequencies have been measured on single slot resonatrs in unilateral fin-line configuration for centered. and off-centrec! fin k,cation:- at X- and i;n-brinds pnd verified with theory. evvriments have ben repeated en bilateralfin-i Inc resonators and compared with the computed resonant frequencies. Fairly T.00d. aqreemont is found between theory and experiment in all tnesc

7 CONTENTS Pae, CH/CPTER INTRODUCTION Characteristics of Slot Lines Review of Slot Resonators Characteristics of Fin-Lines Review of Fin-Line Resonators Scope and Organisatin of the Thesis References 22 CHAPTER 2 ANALYSIS OF SLOT RESONATORS IN FIN-LINE AND OPEN CONFIGURATIONS 2.1 Introduction Analysis of Sin;;le Slot Resonator in Unilateral Fin-Line Configuration Open Slot Resonator Coupled Slot Resonators in Unilateral Fin-Line Configuration Parallel-coupling Parallel-offset coupling End-coupling Coupled Slot Resonators in Open Configuration Bilateral Fin-Line Resonator Odd-mode excitation Even-mode excitation Broadside-Coupled Slot-Resonators in Open Configuration Coupled Resonators in Bilateral Fin-Line Broadside edge-coupled resonators 61 (a) Parallel-coupling 61 (b) Parallel-offset coupling Broadside end-coupled resonators Broadside-Coupled Resonators in Fin-Line Using Two Dielectric Substrates with an Intervening Air-Gap

8 2.9.1 Single resonator un each substrate 63 (a) Fins facinl each other 63 CO Fins facing the sidewalls Broadside edge-coupled resonators 66 (a) Fins facing each other 67 (L) Fins facing the side-walls Broadside end-coupled resonators 67 (a) Fins facing each other 68 (b) Fins facing the side-walls Conclusion C8 References 70 CHAPTER 3 RESONANCE ChARACTERISTICS OF SINGLE-SLOT RESONATOR IN FIN-LINE AND OPEN CONFIGURA- TIONS - NUMERICAL RESULTS 3.1 Resonance Characteristics of Open Slot Resonator Fin-Line Wavelength Single Slot Resonator in Unilateral Fin-Line with Centered Fins Resonant frequency in the Ka-Land Resonant frequency in the X-Land Single Slut Resonator in Unilateral Fin-Line with Off-Centered Fins Resonant frequency in the Ka-Land Resonant frequency in the X-band Conclusion 84 References 86 CHAPTER 4 RESONANCE CHARACTERISTICS OF COUPLED SLOT RESONATORS IN UNILATERAL FIN-LINE AND OPEN CONFIGURATIONS - NUMERICAL RESULTS 4.1 Coupled Slut Resonators in Open Configuration (a) (b) (c) Parallel-coupling Parallel-offset coupling End-coupling u On -J

9 4.2 C9upled Resonators in Unilateral Fin-Line 90 with Centered Fins Resonant frequencies in the Ka-band 91 (a) Parallel-coupling 91 (U) Parallel-offset coupling 92 ((c) End-coupling Resonant frequencies in the X-Land Coupled Resonators in Unilateral Fin-Line with Off-Centered Fins 94 (a) Parallel-coupling 95 (L) Parallel-offset coupling 95 (c) End-coupling End-Effects in Unilateral Fin-Line Coupled Resonators 97 (a) Parallel-coupling 98 (;) Parallel-offset couplinp 99 (c) End-coupling Conclusion 102 References 103 CHAPTER 5 RESONANCE CHARACTERISTICS OF BROADSIDE- COUPLED AND BROADSIDE EDGE-COUPLED SLOT RESONATORS - NUMERICAL RESULTS 5.1 Broadside-Coupled Slot Resonators in Open Configuration Bilateral Fin-Line Resonator 105 (a) Lilateral fin-line wavelength 105 (L) Resonance characteristics in the X-hand 105 (c) Resonance characteristics in the Ka-Land Coupled Resonators in Bilateral Fin-Line 107 5,3.1 Broadside edge-coupled resonators 108 (a) Parallel-coupling 108 Parallel-offset coupling Broadside end-coupled resonators Broadside-Coupled Resonators in Fin-Line Usinp Two Dielectric Substrates with an Intervening Air-Cap 109

10 5.4.1 Single resonator on each substrate 109 (a) Fins facing the sidewalls 110 (L) Fins facinp, each other Broadside edge-coupled resonators with fins facin the sidewalls 111 (a) Parallel-coupling 112 (b) Parallel-offset coupling broadside end-coupled resonators with fins facing the sidewalls Broadside edge-coupled and broadside end-coupled resonators with fins facing each other Conclusion 115 References 117 CHAPTER 6 MEASUREMENT OF RESONANT FREQUENCY AND COMPARISON WITE THEORY 6.1 Measurement Techniques Set up for the measurement of resonant frequency of an open slot resonator Choice of slut width for the slot resonator Set up for the measurement cf resonant frequency of fin-line resonators Measurement of resonant frequency and comparison with theory Open slot resonators Fin-line resonators for the X-Land 125 (a) Unilateral fin-line with centered fins 126 (b) Unilateral fin-line with off-centered fins 127 (c) Bilateral fin-line 130 (j) Fin-line using two dielectric substrates with an intervening air-gap Fin-line resonators for the Ka-band Conclusion 132 References 136 CONCLUSIONS 137 APPENDIX 1 ELECTRIC AND WaZTIC FIELDS IN TERMS OF SCALAR POTENT IALS 144 :IUDATA 147